PYQ Vault

Day 39: CBSE Class 12 Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Application of Integrals. This type asked 3 times: 2024, 2025, 2026. This one: 2026

    10
    The area bounded by the curve y=x∣x∣y = x\left| x \right|, xx-axis and the ordinates x=−1x = -1 and x=1x = 1 is given by

    Tap an option to check your answer.

  2. Question 2

    Continuity and Differentiability. This type asked 3 times: 2024, 2025, 2026. This one: 2026

    22 (a)
    Differentiate xxx^x with respect to xlog⁡xx \log x.

  3. Question 3

    Continuity and Differentiability. This type asked 3 times: 2023, 2024, 2026. This one: 2026

    33 (a)
    If yx2+1=log⁡x2+1−xy\sqrt{x^2 + 1} = \log \sqrt{x^2 + 1} - x, show that (x2+1) dydx+xy+1=0(x^2 + 1)\,\dfrac{dy}{dx} + xy + 1 = 0.

  4. Question 4

    Continuity and Differentiability. This type asked 3 times: 2023, 2024, 2026. This one: 2026

    21
    If x=t+1tx = t + \dfrac{1}{t} and y=t−1ty = t - \dfrac{1}{t}, find dydx\dfrac{dy}{dx} at t=2t = 2.

  5. Question 5

    Continuity and Differentiability. This type asked 3 times: 2023, 2025, 2026. This one: 2026

    35
    If x=a(sin⁡t−tcos⁡t)x = a(\sin t - t \cos t) and y=b(cos⁡t+tsin⁡t)y = b(\cos t + t \sin t), then find dydx\frac{dy}{dx} and d2ydx2\frac{d^2y}{dx^2}.